Physical Review A

Feshbach resonances and transition rates for cold homonuclear collisions between K39 and K41 atoms

Marius Lysebo, Leif Veseth

Published Mar 10, 2010• 56 citations

Abstract

We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$. The $s$-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the ${\mathrm{K}}_{2}$ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.

DOI: 10.1103/physreva.81.032702

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Aug 4, 20211 citation

Physical Review A

Feshbach resonances and transition rates for cold homonuclear collisions between K39 and K41 atoms

Marius Lysebo, Leif Veseth

Published Mar 10, 2010• 56 citations

Publisher

Abstract

^{39}\mathrm{K}

and

^{41}\mathrm{K}

. The

s

-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the

{\mathrm{K}}_{2}

molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.

DOI: 10.1103/physreva.81.032702

Related papers

Properties of cold collisions of K39 atoms and of K41 atoms in relation to Bose-Einstein condensation

H. M. J. M. Boesten, J. M. M. J. Vogels, J. G. C. Tempelaars +1 more

We have determined properties of cold $^{39}\mathrm{K}$ + $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$ + $^{41}\mathrm{K}$ collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited $^{39}\mathrm{K}$ singlet and triplet bound states. We predict positive scattering lengths for the $^{39}\mathrm{K}$ + $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$ + $^{41}\mathrm{K}$ singlet potentials, as well as for the $^{41}\mathrm{K}$ + $^{41}\mathrm{K}$ triplet potential, and a negative value for $^{39}\mathrm{K}$ + $^{39}\mathrm{K}$ triplet scattering. From a study of the magnetic field dependence we conclude that $^{41}\mathrm{K}$ may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the $f=1$ , ${m}_{f}=\ensuremath{-}1$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.We have determined properties of cold $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ and $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited $^{39}\mathrm{K}$ singlet and triplet bound states. We predict positive scattering lengths for the $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ and $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ singlet potentials, as well as for the $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ triplet potential, and a negative value for $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ triplet scattering. From a study of the magnetic field dependence we conclude that $^{41}\mathrm{K}$ may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the $f=1$, ${m}_{f}=\ensuremath{-}1$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.

Physical Review ANov 1, 199632 citations

Feshbach resonances in potassium Bose-Bose mixtures

Luca Tanzi, Cesar R. Cabrera, J. Sanz +3 more

We present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic $^{39}\mathrm{K}\text{\ensuremath{-}}^{41}\mathrm{K}$ mixtures. These are assigned to $s$ -wave molecular channels by comparison to an asymptotic bound state model and coupled-channel calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$ . In particular, we characterize the parameters of a selected $^{39}\mathrm{K}$ Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.We present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic $^{39}\mathrm{K}\text{\ensuremath{-}}^{41}\mathrm{K}$ mixtures. These are assigned to $s$-wave molecular channels by comparison to an asymptotic bound state model and coupled-channel calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$. In particular, we characterize the parameters of a selected $^{39}\mathrm{K}$ Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.

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arXiv:0705.3036New Journal of PhysicsJul 11, 2007197 citations

Ab initiocalculation of Feshbach resonances in cold atomic collisions: s - and p -wave Feshbach resonances in L6i2

Marius Lysebo, Leif Veseth

We present a model applicable to cold diatomic collisions and solve the close-coupled equations for the particular ${^{6}\text{L}\text{i}}_{2}$ system. Feshbach resonances are determined ab initio for both $s$ and $p$ waves. The $s$ -wave scattering lengths are reported for all possible hyperfine states as a function of magnetic field strengths between 0 and 1500 G. In addition, $p$ -wave scattering lengths are calculated for selected hyperfine states. Matrix elements for the hyperfine, Zeeman, and rotational Hamiltonian were worked out by the use of the molecular Hund's case (a) basis set. All relevant matrix elements are reported. The short-range hyperfine interaction has been included in the calculations, and its effect on the scattering length are investigated. Hyperfine parameters were obtained from separate ab initio calculations.We present a model applicable to cold diatomic collisions and solve the close-coupled equations for the particular ${^{6}\text{L}\text{i}}_{2}$ system. Feshbach resonances are determined ab initio for both $s$ and $p$ waves. The $s$-wave scattering lengths are reported for all possible hyperfine states as a function of magnetic field strengths between 0 and 1500 G. In addition, $p$-wave scattering lengths are calculated for selected hyperfine states. Matrix elements for the hyperfine, Zeeman, and rotational Hamiltonian were worked out by the use of the molecular Hund's case (a) basis set. All relevant matrix elements are reported. The short-range hyperfine interaction has been included in the calculations, and its effect on the scattering length are investigated. Hyperfine parameters were obtained from separate ab initio calculations.

Physical Review AJun 5, 200913 citations

Feshbach resonances in cold collisions of potassium atoms

Arturo Bambini, S. Geltman

In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole ${C}_{6}$ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}.$ Our results demonstrate that there is a range of ${C}_{6}$ values for which the collision of two ${}^{39}\mathrm{K}$ atoms displays a single resonance, while for other values of ${C}_{6}$ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two ${}^{41}\mathrm{K}$ atoms for almost all values of the dispersion coefficient ${C}_{6}$ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two ${}^{41}\mathrm{K}$ atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole ${C}_{6}$ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}.$ Our results demonstrate that there is a range of ${C}_{6}$ values for which the collision of two ${}^{39}\mathrm{K}$ atoms displays a single resonance, while for other values of ${C}_{6}$ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two ${}^{41}\mathrm{K}$ atoms for almost all values of the dispersion coefficient ${C}_{6}$ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two ${}^{41}\mathrm{K}$ atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.

Physical Review AJun 4, 20027 citations

Tunable Feshbach resonances and interaction potentials between $^{23}$ Na and $^{87}$ Rb atomsTunable Feshbach resonances and interaction potentials between $^{23}$Na and $^{87}$Rb atoms

Zhichao Guo, Fan Jia, Bin Zhu +3 more

We measure the binding energies of weakly bound Feshbach molecules formed between \Na and \Rb atoms in their lowest hyperfine Zeeman levels. We form molecules at the Feshbach resonance near 347.64 G and dissociate them by magnetic field modulation. We use the binding energies to refine the singlet and triplet potential energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe 10 additional $s$ -wave Feshbach resonances for \Na and \Rb in different combinations of Zeeman sublevels of the $F = 1$ hyperfine states. Some of the resonances show 2-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.We measure the binding energies of weakly bound Feshbach molecules formed between \Na and \Rb atoms in their lowest hyperfine Zeeman levels. We form molecules at the Feshbach resonance near 347.64 G and dissociate them by magnetic field modulation. We use the binding energies to refine the singlet and triplet potential energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe 10 additional $s$-wave Feshbach resonances for \Na and \Rb in different combinations of Zeeman sublevels of the $F = 1$ hyperfine states. Some of the resonances show 2-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.

Aug 4, 20211 citation

^{39}\mathrm{K}

and

^{41}\mathrm{K}

. The

s

{\mathrm{K}}_{2}

We have determined properties of cold

^{39}\mathrm{K}

^{39}\mathrm{K}

and

^{41}\mathrm{K}

^{41}\mathrm{K}

collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited

^{39}\mathrm{K}

singlet and triplet bound states. We predict positive scattering lengths for the

^{39}\mathrm{K}

^{39}\mathrm{K}

and

^{41}\mathrm{K}

^{41}\mathrm{K}

singlet potentials, as well as for the

^{41}\mathrm{K}

^{41}\mathrm{K}

triplet potential, and a negative value for

^{39}\mathrm{K}

^{39}\mathrm{K}

triplet scattering. From a study of the magnetic field dependence we conclude that

^{41}\mathrm{K}

may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the

f=1

, ${m}_{f}=\ensuremath{-}1$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.

s

-wave molecular channels by comparison to an asymptotic bound state model and coupled-channel calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in

^{39}\mathrm{K}

and

^{41}\mathrm{K}

. In particular, we characterize the parameters of a selected

^{39}\mathrm{K}

Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.

We present a model applicable to cold diatomic collisions and solve the close-coupled equations for the particular

{^{6}\text{L}\text{i}}_{2}

system. Feshbach resonances are determined ab initio for both

s

and

p

waves. The

s

-wave scattering lengths are reported for all possible hyperfine states as a function of magnetic field strengths between 0 and 1500 G. In addition,

p

-wave scattering lengths are calculated for selected hyperfine states. Matrix elements for the hyperfine, Zeeman, and rotational Hamiltonian were worked out by the use of the molecular Hund's case (a) basis set. All relevant matrix elements are reported. The short-range hyperfine interaction has been included in the calculations, and its effect on the scattering length are investigated. Hyperfine parameters were obtained from separate ab initio calculations.

{C}_{6}

term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species

{}^{39}\mathrm{K}

{}^{41}\mathrm{K}.

Our results demonstrate that there is a range of

{C}_{6}

values for which the collision of two

{}^{39}\mathrm{K}

atoms displays a single resonance, while for other values of

{C}_{6}

no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two

{}^{41}\mathrm{K}

atoms for almost all values of the dispersion coefficient

{C}_{6}

in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two

{}^{41}\mathrm{K}

atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.

Tunable Feshbach resonances and interaction potentials between

^{23}

Na and

^{87}

Rb atoms

s

-wave Feshbach resonances for \Na and \Rb in different combinations of Zeeman sublevels of the

F = 1

hyperfine states. Some of the resonances show 2-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.